ION GNSS 2012
Session E6: Precise Point Positioning 2

Title: RTK-PPP Algorithms using GNSS Observables from Few Satellites
Author(s): A. Chabata, Y. Suzuki, Y. Kubo and S. Sugimoto, Ritsumeikan University, Japan
Date/Time: Friday, September 21, 2012, 2:58 p.m.
Room: 209/210 (NCC)

In this paper, we present RTK-PPP (Real Time Kinematic - Precise Point Positioning) algorithms using GNSS observables from few available satellites. Namely, we propose the practical GNSS navigation algorithms for automobiles which move on the street in the urban canyon.
We have already developed PPP algorithms based on GR (Gnss Regression) models [3]-[5]. Our RTK precise point positioning algorithm achieved the positioning accuracy in decimeter level. The algorithm does not require the real-time transmitted information such as from WAAS etc. Therefore our PPP algorithm can be easily implemented without any external online received data. However, in order to maintain high precision positioning and navigation with GNSS, detection of cycle slips and multipath is naturally very important. Thus we had presented the detection of cycle slips and multipath based on the statistical test of innovation processes in Kalman filtering. In order to estimate the unknown value such as the position, velocity and ambiguity, the Kalman filter is applied and the cycle slip detection is implemented by using the likelihood ratio test for the byproduct of positioning, namely, the innovation process of the Kalman filter. If a cycle slip occurs, then the mean value of the innovation process changes from zero to an unknown value. Therefore, we can formulate two hypotheses such that the change in the mean value of the innovation process does not occur (null hypothesis), and the change occurs (alternative hypothesis). The decision is therefore based on the likelihood ratio test [1]-[2]. After detecting the received signals with cycle slips and multipath from the GNSS satellites, we remove these measurement data of pseudoranges and L1 and L2 carrier phases, and correct integer ambiguities in the possible occasion. In the urban area, therefore, we often obtain GNSS observables from very few available satellites. In this paper we propose practical RTK-PPP algorithms for such circumstance.

The proposed RTK-PPP algorithm using GNSS observables from few available satellites is based on the constraint of the automobile position for the up direction in the locally level coordinate system?LLCS?, or ENU (east, north, up) coordinates [6], instead of using the WGS-84 coordinate system. The constraint of the automobile position for the up direction in LLCS is provided by the form of additional measurement data to GNSS observables such as pseudoranges and L1 and L2 carrier phases. Also the statistical moving models of automobiles are very important for estimating the automobile position. The moving models of accelerations for the east and north coordinates, and of the velocity for the up coordinate of the automobile are assumed as first order Markov models, respectively [5]. Namely, the east and north coordinates of the automobile are assume respectively as the so-called Singer´s moving model.

Finally experimental results of the data received by the automobile on the road as well as on the street in the urban area, Shinjuku, Tokyo, are shown for the feasibility and usefulness of our RTK-PPP algorithms using GNSS Observables from few satellites.

References: [1] Y. Kubo, K. Sone and S. Sugimoto: Cycle Slip Detection and Correction for Kinematic GPS Based on Statistical Test of Innovation Processes, Proc. of 17th Int. Tech. Meeting of the Satellite Div. of the Institute of Navigation (ION GNSS 2004), pp. 1438-1447, Long Beach, CA, 21-24 Sept. (2004). [2] M. Kamimura, R. Tomita, T. Nagano, A. Chabata, Y. Kubo and Sueo Sugimoto: Detection of Cycle Slips and Multipath in GNSS RTK Precise Point Positioning, Proc. 24th Int. Tech. Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2011), pp. 1056-1067, Portland, Oregon, Sept., 2011. [3] S. Sugimoto and Y. Kubo: GNSS Regressive Models and Precise Point Positioning, Proc. 36th ISCIE International Symposium on Stochastic Systems Theory and Its Applications, pp. 159-164, Saitama, Japan, Oct., 2004. [4] S. Sugimoto and Y. Kubo: Unified Methods of Point and Relative Positioning Based on GNSS Regression Equations, Proc. 19th Int. Tech. Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2006), pp. 345-358, Fort Worth, Texas, Sep., 2006. [5] S. Sugimoto and R. Shibasaki (Eds.): GPS Handbook (in Japanese), Asakura-Shoten, Tokyo (2010). [6] B. Hofmann-Wellenhof, H. Lichtenegger and J. Collins: GPS Theory and Practice, 5th revised edition, Springer-Verlag (2001).

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